Home
Class 12
MATHS
If f"(x) > 0 and f(1) = 0 such that g(x)...

If f"(x) > 0 and f(1) = 0 such that `g(x) = f(cot^2x + 2cotx + 2) where 0 < x < pi`, then g'(x) decreasing in (a, b). where `a + b + pi/4`…

A

`(0,pi)`

B

`((pi)/(2),pi)`

C

`((3pi)/(4),pi)`

D

`(0,(3pi)/(4))`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|35 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos
  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

if f'(x) = 3x^2-2/x^3 and f(1)=0 , find f(x).

If f(x) = 2x - 5, then f (0) is :

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f be a function such that f(xy) = f(x).f(y), AA y in R and R(1 + x) = 1 + x(1 + g(x)) . where lim_(x rarr 0) g(x) = 0 . Find the value of int_(1)^(2) (f(x))/(f'(x)).(1)/(1+x^(2))dx

Statement-1 If A = {x |g(x) = 0} and B = {x| f(x) = 0}, then A nn B be a root of {f(x)}^(2) + {g(x)}^(2)=0 Statement-2 x inAnnBimpliesx inAorx inB .

Let g(x) = ln f(x) where f(x) is a twice differentiable positive function on (0, oo) such that f(x+1) = x f(x) . Then for N = 1,2,3 g''(N+1/2)- g''(1/2) =

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

Find f'(x), where: f(x) = cos(Iogx)^2 where x > 0

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f"(x) > 0 and f(1) = 0 such that g(x) = f(cot^2x + 2cotx + 2) where...

    Text Solution

    |

  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) to vec R be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , ...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

    Text Solution

    |

  7. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  8. A vertical line passing through the point (h,0) intersects th ellipse ...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. The total number of local maxima and local minima of the function f(x)...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  15. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which has local maximum at x=-1 . If f(2)...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |